1 Data

participant_id q_id creature dataset scale response qtext true_value
0f7fc4ff03ad53f80b84cc62c1644648 Q0 ewok dataset1 log2 10000 Between 30 and 40 ABY, how does the population of Ewoks change? NA
0f7fc4ff03ad53f80b84cc62c1644648 QE1 ewok dataset1 log2 500 What is the population of Ewoks in 10 ABY? 481.62
0f7fc4ff03ad53f80b84cc62c1644648 QE2 ewok dataset1 log2 24 In what ABY does the population of Ewoks reach 4,000? 28.45
0f7fc4ff03ad53f80b84cc62c1644648 QI2 ewok dataset1 log2 16 How many times more Ewoks are there in 40 ABY than in 20 ABY? 10.69
0f7fc4ff03ad53f80b84cc62c1644648 QI3 ewok dataset1 log2 6 How long does it take for the population of Ewoks in 10 ABY to double? 6.25
0f7fc4ff03ad53f80b84cc62c1644648 QI1 ewok dataset1 log2 14848 From 20 ABY to 40 ABY, the population increases by ____ Ewoks. 14363.34

2 Q0: Open Ended

q_id creature qtext true_value
Q0 tribble Between stardates 4530 and 4540, how does the population of Tribbles change? NA
Q0 ewok Between 30 and 40 ABY, how does the population of Ewoks change? NA

2.1 Linear Scale

## NULL

2.2 Log Scale

## NULL

3 QE1: Estimate a population given a year

3.1 Question

q_id creature qtext true_value
QE1 tribble What is the population of Tribbles in stardate 4510? 481.62
QE1 ewok What is the population of Ewoks in 10 ABY? 481.62

3.2 Closest Points

x y0 dataset y
3010 481.62 dataset1 445.48
3010 481.62 dataset2 466.90

3.3 Exploration

3.4 Data

QE1 data set example
participant_id dataset scale response true_value deviation abs_deviation closest_pt_value closest_pt_deviation closest_pt_abs_deviation
0f7fc4ff03ad53f80b84cc62c1644648 dataset1 log2 500 481.62 18.38 18.38 445.48 54.52 54.52
0f7fc4ff03ad53f80b84cc62c1644648 dataset2 linear 500 481.62 18.38 18.38 466.90 33.10 33.10
5b16d305db2092ddae8cf1c410341f36 dataset1 log2 500 481.62 18.38 18.38 445.48 54.52 54.52
5b16d305db2092ddae8cf1c410341f36 dataset2 linear 400 481.62 -81.62 81.62 466.90 -66.90 66.90
8ab3438eb60817740bdd15143ceacd06 dataset2 log2 510 481.62 28.38 28.38 466.90 43.10 43.10
8ab3438eb60817740bdd15143ceacd06 dataset1 linear 800 481.62 318.38 318.38 445.48 354.52 354.52

3.5 Common Responses

3.6 Wilcox

3.6.1 True value absolute deviation

scale variable n median iqr
linear abs_deviation 307 381.62 463.23
log2 abs_deviation 306 22.89 12.00 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abs_deviation by scale
## Kruskal-Wallis chi-squared = 164.28, df = 1, p-value < 2.2e-16
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  abs_deviation by scale
## W = 74734, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

3.6.2 Closest point absolute deviation

scale variable n median iqr
linear closest_pt_abs_deviation 307 345.48 410.88
log2 closest_pt_abs_deviation 306 45.10 21.41 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  closest_pt_abs_deviation by scale
## Kruskal-Wallis chi-squared = 207.1, df = 1, p-value < 2.2e-16
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  closest_pt_abs_deviation by scale
## W = 78421, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

4 QE2: Estimate a year given a population

4.1 Question

q_id creature qtext true_value
QE2 tribble In what stardate does the population of Tribbles reach 4,000? 4528.45
QE2 ewok In what ABY does the population of Ewoks reach 4,000? 28.45

4.2 Closest Points

x y0 dataset y
27 3369.38 dataset1 3010.82
25 2661.12 dataset1 3064.85
26 2994.03 dataset1 3169.40
28 3792.59 dataset1 3228.14
24 2365.86 dataset1 3774.90
30 4807.77 dataset1 5174.12
25 2661.12 dataset2 2746.12
28 3792.59 dataset2 3859.22
27 3369.38 dataset2 4099.69
29 4269.76 dataset2 4423.01

4.3 Exploration

4.4 Data

QE2 data set example
participant_id dataset scale response true_value deviation abs_deviation closest_pt_value closest_pt_deviation closest_pt_abs_deviation
0f7fc4ff03ad53f80b84cc62c1644648 dataset1 log2 24 28.45 -4.45 4.45 24 0 0
0f7fc4ff03ad53f80b84cc62c1644648 dataset2 linear 27 28.45 -1.45 1.45 27 0 0
5b16d305db2092ddae8cf1c410341f36 dataset1 log2 24 28.45 -4.45 4.45 24 0 0
5b16d305db2092ddae8cf1c410341f36 dataset2 linear 25 28.45 -3.45 3.45 27 -2 2
8ab3438eb60817740bdd15143ceacd06 dataset2 log2 28 28.45 -0.45 0.45 27 1 1
8ab3438eb60817740bdd15143ceacd06 dataset1 linear 28 28.45 -0.45 0.45 24 4 4

4.5 Common Responses

4.6 Wilcox

4.6.1 True value absolute deviaiton

scale variable n median iqr
linear abs_deviation 305 3.45 3
log2 abs_deviation 309 2.45 3 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abs_deviation by scale
## Kruskal-Wallis chi-squared = 0.61702, df = 1, p-value = 0.4322
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  abs_deviation by scale
## W = 48841, p-value = 0.4323
## alternative hypothesis: true location shift is not equal to 0

4.6.2 Closest point absolute deviation

scale variable n median iqr
linear closest_pt_abs_deviation 305 1 1
log2 closest_pt_abs_deviation 309 1 2 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  closest_pt_abs_deviation by scale
## Kruskal-Wallis chi-squared = 5.2256, df = 1, p-value = 0.02226
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  closest_pt_abs_deviation by scale
## W = 42390, p-value = 0.02227
## alternative hypothesis: true location shift is not equal to 0

5 QI1: Estimate an additive increase in population between two years

q_id creature qtext true_value
QI1 tribble From 4520 to 4540, the population increases by ____ Tribbles. 14363.34
QI1 ewok From 20 ABY to 40 ABY, the population increases by ____ Ewoks. 14363.34

5.1 Closest Points

dataset 3020 3040 increase
dataset1 1529.18 17046.94 15517.75
dataset2 1288.91 24186.34 22897.43

5.2 Exploration

5.3 Data

QI1 data set example
participant_id dataset scale response true_value deviation abs_deviation closest_pt_value closest_pt_deviation closest_pt_abs_deviation
0f7fc4ff03ad53f80b84cc62c1644648 dataset1 log2 14848 14363.34 484.66 484.66 15517.75 -669.75 669.75
0f7fc4ff03ad53f80b84cc62c1644648 dataset2 linear 23000 14363.34 8636.66 8636.66 22897.43 102.57 102.57
5b16d305db2092ddae8cf1c410341f36 dataset1 log2 13000 14363.34 -1363.34 1363.34 15517.75 -2517.75 2517.75
5b16d305db2092ddae8cf1c410341f36 dataset2 linear 2400 14363.34 -11963.34 11963.34 22897.43 -20497.43 20497.43
8ab3438eb60817740bdd15143ceacd06 dataset2 log2 14800 14363.34 436.66 436.66 22897.43 -8097.43 8097.43
8ab3438eb60817740bdd15143ceacd06 dataset1 linear 13500 14363.34 -863.34 863.34 15517.75 -2017.75 2017.75

5.4 Common Responses

5.5 Wilcox

5.5.1 True value absolute deviaiton

scale variable n median iqr
linear abs_deviation 305 3036.66 8500.00
log2 abs_deviation 307 1363.34 11331.84 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abs_deviation by scale
## Kruskal-Wallis chi-squared = 6.1615, df = 1, p-value = 0.01306
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  abs_deviation by scale
## W = 52243, p-value = 0.01306
## alternative hypothesis: true location shift is not equal to 0

5.5.2 Closest point absolute deviation

scale variable n median iqr
linear closest_pt_abs_deviation 305 1517.75 9379.68
log2 closest_pt_abs_deviation 307 1987.57 7430.25 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  closest_pt_abs_deviation by scale
## Kruskal-Wallis chi-squared = 0.61268, df = 1, p-value = 0.4338
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  closest_pt_abs_deviation by scale
## W = 45106, p-value = 0.4339
## alternative hypothesis: true location shift is not equal to 0

6 QI2: Estimate a multiplicative change in population between two years (i.e. how many times larger)

q_id creature qtext true_value
QI2 tribble How many times more Tribbles are there in 4540 than in 4520? 10.68524
QI2 ewok How many times more Ewoks are there in 40 ABY than in 20 ABY? 10.68524

6.1 Closest Points

dataset 3020 3040 increase
dataset1 1529.18 17046.94 11.15
dataset2 1288.91 24186.34 18.76

6.2 Exploration

6.3 Data

QI2 data set example
participant_id dataset scale response true_value deviation abs_deviation closest_pt_value closest_pt_deviation closest_pt_abs_deviation
0f7fc4ff03ad53f80b84cc62c1644648 dataset1 log2 16.0 10.69 5.31 5.31 11.15 4.85 4.85
0f7fc4ff03ad53f80b84cc62c1644648 dataset2 linear 17.0 10.69 6.31 6.31 18.76 -1.76 1.76
5b16d305db2092ddae8cf1c410341f36 dataset1 log2 32.0 10.69 21.31 21.31 11.15 20.85 20.85
5b16d305db2092ddae8cf1c410341f36 dataset2 linear 500.0 10.69 489.31 489.31 18.76 481.24 481.24
8ab3438eb60817740bdd15143ceacd06 dataset2 log2 11.6 10.69 0.91 0.91 18.76 -7.16 7.16
8ab3438eb60817740bdd15143ceacd06 dataset1 linear 12.5 10.69 1.81 1.81 11.15 1.35 1.35

6.4 Common Responses

6.5 Wilcox

6.5.1 True value absolute deviaiton

scale variable n median iqr
linear abs_deviation 307 5.32 11.13
log2 abs_deviation 306 5.32 8.55 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abs_deviation by scale
## Kruskal-Wallis chi-squared = 9.2616, df = 1, p-value = 0.00234
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  abs_deviation by scale
## W = 53638, p-value = 0.002342
## alternative hypothesis: true location shift is not equal to 0

6.5.2 Closest point absolute deviation

scale variable n median iqr
linear closest_pt_abs_deviation 307 5.85 9.61
log2 closest_pt_abs_deviation 306 3.15 7.01 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  closest_pt_abs_deviation by scale
## Kruskal-Wallis chi-squared = 33.793, df = 1, p-value = 6.131e-09
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  closest_pt_abs_deviation by scale
## W = 59712, p-value = 6.139e-09
## alternative hypothesis: true location shift is not equal to 0

7 QI3: Estimate the number of years necessary to double the population

q_id creature qtext true_value
QI3 tribble How long does it take for the population of Tribbles in stardate 4510 to double? 6.245448
QI3 ewok How long does it take for the population of Ewoks in 10 ABY to double? 6.245448

7.1 Closest Points

From QE1, the estimated population at 10 is:

x y0 dataset y doubled
3010 481.62 dataset1 445.48 890.97
3010 481.62 dataset2 466.90 933.79
x y0 dataset y doubled pop_diff year_diff
3014 747.52 dataset1 786.81 890.97 104.15 4
3013 668.65 dataset1 723.92 890.97 167.04 3
3016 936.72 dataset1 1073.52 890.97 182.55 6
3019 1320.97 dataset1 1074.29 890.97 183.32 9
3016 936.72 dataset2 1028.59 933.79 94.80 6
3013 668.65 dataset2 819.66 933.79 114.13 3
3017 1049.78 dataset2 809.55 933.79 124.25 7
3015 836.45 dataset2 750.03 933.79 183.76 5
3014 747.52 dataset2 735.97 933.79 197.82 4

7.2 Exploration

7.3 Data

QI3 data set example
participant_id dataset scale response true_value deviation abs_deviation closest_pt_value closest_pt_deviation closest_pt_abs_deviation
0f7fc4ff03ad53f80b84cc62c1644648 dataset1 log2 6 6.25 -0.25 0.25 4 2 2
0f7fc4ff03ad53f80b84cc62c1644648 dataset2 linear 10 6.25 3.75 3.75 6 4 4
5b16d305db2092ddae8cf1c410341f36 dataset1 log2 8 6.25 1.75 1.75 4 4 4
5b16d305db2092ddae8cf1c410341f36 dataset2 linear 12 6.25 5.75 5.75 6 6 6
8ab3438eb60817740bdd15143ceacd06 dataset2 log2 7 6.25 0.75 0.75 6 1 1
8ab3438eb60817740bdd15143ceacd06 dataset1 linear 5 6.25 -1.25 1.25 4 1 1

7.4 Common Responses

7.5 Wilcox

7.5.1 True value absolute deviaiton

scale variable n median iqr
linear abs_deviation 306 3.76 4.51
log2 abs_deviation 307 1.25 2.51 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abs_deviation by scale
## Kruskal-Wallis chi-squared = 66.573, df = 1, p-value = 3.371e-16
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  abs_deviation by scale
## W = 64676, p-value = 3.378e-16
## alternative hypothesis: true location shift is not equal to 0

7.5.2 Closest point absolute deviation

scale variable n median iqr
linear closest_pt_abs_deviation 306 4 5.00
log2 closest_pt_abs_deviation 307 1 2.95 

## 
##  Kruskal-Wallis rank sum test
## 
## data:  closest_pt_abs_deviation by scale
## Kruskal-Wallis chi-squared = 65.65, df = 1, p-value = 5.386e-16
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  closest_pt_abs_deviation by scale
## W = 64454, p-value = 5.396e-16
## alternative hypothesis: true location shift is not equal to 0